Problem: Simplify the following expression: $\dfrac{35k^4}{15k^4}$ You can assume $k \neq 0$.
Answer: $ \dfrac{35k^4}{15k^4} = \dfrac{35}{15} \cdot \dfrac{k^4}{k^4} $ To simplify $\frac{35}{15}$ , find the greatest common factor (GCD) of $35$ and $15$ $35 = 5 \cdot 7$ $15 = 3 \cdot 5$ $ \mbox{GCD}(35, 15) = 5 $ $ \dfrac{35}{15} \cdot \dfrac{k^4}{k^4} = \dfrac{5 \cdot 7}{5 \cdot 3} \cdot \dfrac{k^4}{k^4} $ $\phantom{ \dfrac{35}{15} \cdot \dfrac{4}{4}} = \dfrac{7}{3} \cdot \dfrac{k^4}{k^4} $ $ \dfrac{k^4}{k^4} = \dfrac{k \cdot k \cdot k \cdot k}{k \cdot k \cdot k \cdot k} = 1 $ $ \dfrac{7}{3} \cdot 1 = \dfrac{7}{3} $